The correct thing to do is solder it. You can use lower-temp solders than silver solder - Brownells' Hi-Temp, Hi-Force 44 is a lower-temp solder than true silver solder that works well in situations like this:

Real silver solder needs over 1100 degrees F to melt. That's to the point where you've pulled most any hardness out of steel. At 645F, you're in the range where you're leaving some heat treatment in the steel.